First, your questions:
do you say increase in "a number of cars" or "the number of cars"?
the number of cars
and is it "an increase in~" or just "increase in~"
an increase in
This article "a/an, the" is driving me crazy lol!!
That's very common! Stick with it, and read as much English as you can so that the difference will start to sound normal to you.
f you say "fuel efficent cars", does that also imply to you that
it would be cost efficent as well since they are renewable energies(?) or whatever.
Not necessarily. At present, hybrid vehicles, which are extremely fuel-efficient, are extremely expensive. You could argue, however, that the combination of advances in hybrid technology and economies of scale gained as demand for these cars increases will, over time, lead them to be less expensive and thereby more cost-effective.
Now, let's look at grammar.
You write:Cars have been perceived as one of the greatest human inventions for its convinence and far traveling distances.
Notice that "cars" -- which is plural -- is the subject of the sentence. But then you use the pronoun "it" to stand in for the subject later in the sentence. This creates a mismatch. Instead, say:Cars have been perceived as one of the greatest human inventions for
theirconvenience and
ability to travel far distances.